X-Ray Bursts and Millisecond Oscillations in the
Millisecond X-Ray Pulsar SAX J1808.4-3658
Deepto Chakrabarty
Massachusetts Institute of Technology
Collaborators:
Edward H. Morgan (MIT)
Michael P. Muno (MIT)
Duncan K. Galloway (MIT)
Rudy Wijnands (St. Andrews)
Michiel van der Klis (Amsterdam)
Craig Markwardt (NASA/GSFC)
Millisecond Variability in Low-Mass X-Ray Binaries
1.
Kilohertz quasi-periodic oscillations (kHz QPOs)
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QPO pairs with roughly constant frequency separation (~300 Hz)
QPO frequencies drift by hundreds of Hz as X-ray flux changes
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Particular separation frequency is a characteristic of a given source
Seen in over 20 LMXBs. Believed to originate in accretion disk.
2.
X-ray burst oscillations
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Nearly coherent msec oscillations during thermonuclear bursts (270-619 Hz)
Frequency drifts by several Hz during burst, reaching an asymptotic maximum that is a
characteristic of a given source. Interpreted as angular momentum conservation in decoupled
burning layer on rotating NS (Strohmayer et al. 1997; Cumming & Bildsten 2000).
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–
Seen in 10 sources, over 100 examples (e.g. Muno et al. 2002); most are also kHz QPO sources
Amplitude evolution in burst rise interpreted as spreading hot spot on rotating NS.
Oscillations in tail not well understood.
“Nuclear-powered” pulsars?
–
3.
“Bona fide” accretion-powered millisecond X-ray pulsars
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Four sources known, all X-ray transients in very compact binaries
Pulsed amplitude ~5%, why not detected in other LMXBs?
(1)+(2) often seen together, but neither seen together with (3). Thus, relationship with spin not proven directly.
Relationship Between Burst Oscillations and kHz QPOs
The separation frequency ∆nkHz organizes the burst oscillation sources into two
groups:
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•
“Slow” oscillators (~300 Hz):
“Fast” oscillators (~600 Hz):
nburst ≈ ∆nkHz
nburst ≈ 2∆nkHz
Photospheric radius expansion properties also divide along these lines, with
fast oscillations usually occuring in radius expansion bursts. (Muno et al. 2000)
Which is spin frequency, nburst or ∆nkHz ? Factor of two ambiguity.
kHz QPOs: (1) Beat frequency interpretation (e.g. Miller, Lamb, & Psaltis 1998)
Lower kHz QPO = beat between Keplerian and spin frequencies. Requires special burst ignition properties
for fast oscillators. Why is everything spinning at ~300 Hz?
(2) Relativistic precession interpretation (e.g. Stella & Vietri 1999)
Lower kHz QPO = GR precession mode frequency for free-particle orbit at preferred radius. Relationship
to burst oscillation not explained in this picture with additional assumptions.
In both interpretations, upper kHz QPO is Keplerian frequency at “preferred” accretion disk radius
X-Ray Outburst History of SAX J1808.4-3658
•
1996 September (BeppoSAX)
– Source discovered by BeppoSAX/WFC (in ‘t Zand et al. 1998)
– Thermonuclear bursts observed.
– Marginal detection of 401 Hz burst oscillation in later reanalysis (in ‘t Zand et al.
2001)
•
1998 April (RXTE)
– 401 Hz persistent pulsations (Wijnands & van der Klis 1998)
– 2 hr binary orbit (Chakrabarty & Morgan 1998)
– Mass donor is a hydrogen-rich ~0.05 M§ brown dwarf (Bildsten & Chakrabarty 2001)
•
2000 January (RXTE)
– Emerged from behind Sun in low, flaring state (Wijnands et al. 2001)
•
2002 October (RXTE)
– Outburst detected early (Markwardt, Miller, & Wijnands 2002)
2002 Outburst Flux History for SAX J1808.4-3658
X-ray bursts observed
(peak accretion rate ~1% Eddington)
Twin kHZ QPOs
observed
700 ksec total: unprecedented coverage of the decay of a soft X-ray transient
Executive Summary of 2002 Outburst Results for SAX J1808.4-3658
• nburst ≈ 400 Hz
• DnkHz ≈ 200 Hz
• nspin ≈ 400 Hz
(Chakrabarty et al. 2003)
(Wijnands et al. 2003)
(Morgan et al. 2003)
Upper limit on amplitude of a persistent pulsation at 200.5 Hz is <0.014%,
establishing the spin frequency as 401 Hz.
Kilohertz QPO Pair in SAX J1808.4-3658
2002 October 16 data (near peak of outburst)
nspin= 400.975 Hz
n1=499±4 Hz
n2=694±4 Hz
Dn=195±6 Hz
Wijnands et al. 2003
Chakrabarty et al. 2003
X-Ray Burst Oscillations in SAX J1808.4-3658
spin
frequency
Small precursor to Burst 4 on 2002 Oct 19.4
(SAX J1808.4-3658)
Peak count rate of main
burst ~14 kcount/s/PCU
X-Ray Burst Oscillation in SAX J1808.4-3658: detail
drifting
oscillation
burst tail oscillation
•
•
•
•
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Rapidly drifting oscillation in burst rise
in 397-403 Hz range
Oscillation overshoots the spin
frequency during the burst rise.
No oscillation detected during radius
expansion phase of burst
Oscillations reappear in burst tail at
almost exactly the spin frequency, but
larger by 6±1 mHz, which is 0.0015%
(or 1 part in 67000) difference.
Burst oscillation amplitudes vary
between 3% and 5%. No harmonics
are detected (<0.5%).
spin frequency
Burst 3
2002 Oct 18.183
Chakrabarty et al. 2003
Rapid drift of oscillation during burst rise
in SAX J1808.4-3658
spin frequency
•
Drifting oscillation is evidently similar
phenomenon as seen in other 10 burst
oscillation sources, where drift is
interpreted as angular momentum
conservation in a decoupled burning
layer.
•
Oscillation drifts rapidly during the
burst rise, changing by around 5 Hz in
around 0.5 s.
This drift time scale is shorter by an
order of magnitude compared to other
sources.
Phase connection indicates smoothly
varying oscillation.
•
•
Chakrabarty et al. 2003
Chakrabarty et al. 2003
Phase connection of oscillation during burst rise
in SAX J1808.4-3658
Burst 3
2002 Oct 18.183
Independent phase
residuals relative to
constant frequency
model at 400.9752 Hz
Consistent with a single, smoothly drifting burst oscillation
Rapid drift in SAX J1808.4-3658: magnetic field effect?
•
Cumming & Bildsten (2000): sufficiently strong magnetic field may prevent
rotational shearing in burning layer (i.e. when B2/8π is comparable to the shear
energy), leading to small (or zero) frequency drift.
•
Our slightly modified idea: the magnetic field provides a restoring force that
acts to counter the shear, leading to a more rapid drift. We thus interpret the
comparatively rapid drift in SAX J1808.4-3658 as evidence of a stronger
magnetic field than other burst oscillation sources.
•
SAX J1808.4-3658 is only persistent pulsar among the burst oscillation
sources. Others may have fields too weak to channel accretion flow. Compare
proposal of diamagnetic screening of field by accreted material for high
accretion rates (Cumming, Zweibel, & Bildsten 2001). (But, why are spectra similar?)
•
If most burst oscillation sources have weaker magnetic fields, then they are
unlikely to show persistent pulsations down to very low amplitudes.
phase of burst tail
oscillation (sinusoidal)
persistent
pulsation
(accretion)
The oscillations in the burst tail always have the same rotational phase!
They lead the persistent pulsations by about 10%.
Chakrabarty et al. 2003
Phase relationship of burst tail oscillations and persistent pulsations
in SAX J1808.4-3658
Rotational phase-locking of burst tail oscillations
in SAX J1808.4-3658
•
The burst tail oscillations must be associated with the NS surface.
•
The emitting hot spot in the burst tail “knows” about the NS magnetic field
and probably has a nearly fixed orientation with respect to the magnetic poles.
•
The 11% phase offset with respect to the persistent pulsations is consistent
with the phase drift accumulated over the duration of the burst tails due to the
slight (<0.002%) frequency difference. This requires an initial phase
alignment in the burst tail followed by a slight motion of the hot spot (e.g.
Spitkovsky et al. 2002; Heyl 2001).
Energy dependence of oscillations and pulsations
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Most burst oscillation sources (Muno et al. 2003)
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Pulse amplitude increases with energy
Hard pulses lag soft pulses
Persistent millisecond pulsations (SAX J1808.4-3658 and XTE
J0929-314; Cui et al. 1998; Galloway et al. 2002)
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Pulse amplitude decreases (slightly) with energy
Hard pulses precede soft pulses
Burst oscillations in SAX J1808.4-3658 (preliminary!)
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Pulse amplitude roughly constant with energy
No clear pattern in phase vs energy
Further analysis in progress
Burst Oscillation Frequencies
4U 1916-05
270 Hz
4U 1702-429
330 Hz
4U 1728-34
363 Hz
SAX J1808.4-3658
401 Hz
KS 1731-26
524 Hz
Aql X-1
549 Hz
X1658-298
567 Hz
4U 1636-53
581 Hz
X1743-29
589 Hz
SAX J1750.8-2900
601 Hz
4U 1608-52
619 Hz
Distribution of Burst Oscillation Frequencies
Summary
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X-ray bursts in SAX J1808.4-3658 occur in a relatively unexplored
low- M˙ regime.
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Thermonuclear X-ray burst oscillations trace the spin of accreting
neutron stars: nuclear-powered millisecond pulsars.
•
†
We do not understand the origin of kilohertz QPOs.
•
The magnetic field strength of the millisecond X-ray pulsar SAX
J1808.4-3658 is evidently stronger than that of the other (nonpulsing) burst oscillation sources.
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Oscillations in the burst tails of SAX J1808.4-3658 are somehow
tied to the magnetic field geometry of the neutron star.
•
The spin frequency distribution of nuclear-powered millisecond
pulsars cuts off sharply at the high end.